Mensuration — Formula Sheet

White washing / painting / canvas needed → use surface area

Storage / capacity / quantity inside → use volume

Cuboid: LSA=2h(l+b), TSA=2(lb+bh+hl), V=lbh

Cube: LSA=4a^2, TSA=6a^2, V=a^3

Right prism: LSA=Perimeter of base × height, TSA=Lateral surface area+2(area of the end surface), V=area of base × height

Regular circular Cylinder: CSA=2πrh, TSA=2πr(r+h), V=πr^2h

Right pyramid: LSA=1/2 (perimeter of base) × slant height, TSA=Lateral surface area+area of the base, V=1/3 area of the base × height

TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemisphere

TSA of the toy = CSA of hemisphere + CSA of cone

Surface area of combined solids = exposed surface only

The slant height of a conical tent with r=7 m and h=10 m is √149 = 12.2 m.

Its formulas are LSA=2h(l+b), TSA=2(lb+bh+hl), and V=lbh.

Its formulas are LSA=4a^2, TSA=6a^2, and V=a^3.

Its formulas are CSA=2πrh, TSA=2πr(r+h), and V=πr^2h.

Its formulas are CSA=πrl, TSA=πr(l+r), and V=(1/3)πr^2h.

For a sphere of radius r, CSA=TSA=4πr^2 and V=(4/3)πr^3.

For a hemisphere of radius r, CSA=2πr^2, TSA=3πr^2, and V=(2/3)πr^3.